Observer design for nonlinear discrete-time systems : Immersion and dynamic observer error linearization techniques

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Original languageEnglish
Pages (from-to)504-514
Journal / PublicationInternational Journal of Robust and Nonlinear Control
Issue number5
Publication statusPublished - 25 Mar 2010


This paper focuses on the observer design for nonlinear discrete-time systems by means of nonlinear observer canonical form. At first, sufficient and necessary conditions are obtained for a class of autonomous nonlinear discrete-time systems to be immersible into higher dimensional observer canonical form. Then a method called dynamic observer error linearization is developed. By introducing a dynamic auxiliary system, the augmented system is shown to be locally equivalent to the generalized observer form, whose nonlinear terms contain auxiliary states and output of the system. A constructive algorithm is also provided to obtain the state coordinate transformation. These results are an extension of their counterparts of nonlinear continuous-time systems to nonlinear discrete-time systems (Syst. Control Lett. 1986; 7:133-142; SIAM. J. Control Optim. 2003; 41:1756-1778; Int. J. Control 2004; 77:723-734; Automatica 2006; 42:321-328; IEEE Trans. Automat. Control 2007; 52:83-88; IEEE Trans. Automat. Control 2004; 49:1746-1750; Automatica 2006; 42:2195-2200; IEEE Trans. Automat. Control 1996; 41:598-603; Syst. Control Lett. 1997; 31:115-128). © 2009 John Wiley & Sons, Ltd.

Research Area(s)

  • Discrete-time, Nonlinear, Observer